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Full text of "Mathematical And Physical Papers - Iii"

218             ON THE  CONDUCTION  OF  HEAT  IN  CRYSTALS.
and two, those which belong to the same pair being situated at equal distances from the two faces respectively, the isothermal curves belonging to the same temperature in the two systems will be of equal magnitude, provided that the exterior conductivity h have the same value for the two faces. The last condition is satisfied, according to what has been already remarked, when the two faces are covered by a thin coating of the same substance, which regulates the exterior conductivity; but it is probable that it may be satisfied generally even if the faces be left bare, provided that they have the same degree of polish*.
The experiments of M. de Senannont bear directly on the first two cases mentioned above. In the case of crystals which exhibited three different conductivities, it was found that when three plates were cut in the directions of the three principal planes, the ratio of the principal axes of the ellipses formed on one plate, as determined by observation, agreed very closely with the result calculated from the ratios which had previously been determined by observation from the other two plates. An interesting experiment bearing on the second case is described by M. de Senarmont in his second paper (p. 187). A rather thick plate of quartz, inclined to the axis at an angle of 45, was drilled in a direction perpendicular to its plane, and heated by means of a wire inserted into the hole, after its two faces had been covered with wax. The curves marked out on the two faces approximated to the two bases of an elliptic cylinder, symmetrical with respect to the principal plane, and having its axis inclined towards the axis of the crystal, (which in quartz is the direction of greatest conductivity,) so as to cross the wire, which was perpendicular to the plate. The carves however were not elliptical but egg-shaped, having their axes of symmetry situated in the principal plane, the end at which the curvature was least being that which was nearest to the wire, so that the blunt ends on the two faces were turned in opposite directions, the curves being in other respects alike. It will be seen at once that the symmetry of the curves with respect to the principal plane, the obliquity of the line joining their centres,
* This result follows readily from the theory of molecular radiation, according to the suppositions usually made.